3 Mienzaniso yemibvunzo pamusoro pekuwedzera kwenzvimbo
1. Pepa resimbi patembiricha ye20 o C rine urefu hwe50 cm uye upamhi hwe30 cm. Kana coefficient yekuwedzera kwesimbi iri 10 -5 o C -1 saka kuwedzera kwenzvimbo nenzvimbo yese patembiricha ye60 o C….
Kukurukurirana
Zvinozivikanwa kuti:
Tembiricha yekutanga (T 1 ) = 20 o C
Kupisa kwekupedzisira (T2 ) = 60 o C
Kuchinja kwetembiricha (Δ T) = 60 o C – 20 o C = 40 o C
Nzvimbo yekutanga (A 1 ) = Kureba x upamhi = 50 cm x 30 cm = 1500 cm 2
Kuwanda kwesimbi yakabatana (α ) = 10 -5 o C -1
Kuwanda kwesimbi (β ) = 2a = 2 x 10 -5 o C -1
Mubvunzo: Kuwedzera kwenzvimbo (Δ A )
Kuwedzera kwenzvimbo (ΔA ) :
ΔA = β A 1Δ T
ΔA = ( 2 x 10 -5 o C -1 )(1500 cm 2 )(40 o C)
ΔA = (80 x 10 -5 )(1500 cm 2 )
ΔA = 1 20.000 x 10 -5 cm 2
ΔA = 1.2 x 10 5 x 10 -5 cm 2
ΔA = 1.2 cm 2
Nzvimbo yese ( A 2 ):
A 2 = A 1 + Δ A
A 2 = 1500 cm 2 + 1.2 cm 2
A 2 = 1501 , 2 cm 2
2. Ndiro yearuminiyamu ine chiyero chekuwedzera kwemutsara che24 x 10 -6 / o C ine nzvimbo ye40 cm 2 patembiricha ye30 o C. Sarudza tembiricha yekupedzisira kana nzvimbo yendiro yearuminiyamu ikawedzera kusvika 40,2 cm 2.
Kukurukurirana
Zvinozivikanwa kuti:
Tembiricha yekutanga (T 1 ) = 30 o C
Kuwanda kwekuwedzera kwearuminiyamu (α ) = 24 x 10 -6 o C -1
Kukura kwenzvimbo yearuminiyamu (β ) = 2α = 2 x 24 x 10 -6 o C -1 = 48 x 10 -6 o C -1
Nzvimbo yekutanga (A 1 ) = 40 cm 2
Nzvimbo yekupedzisira (A 2 ) = 40,2 cm 2
Kuchinja kwenzvimbo (Δ A) = 40,2 cm 2 – 40 cm 2 = 0,2 cm 2
Mubvunzo: Tsvaga tembiricha yekupedzisira (T 2 )
Mhinduro:
Fomura yekuchinja nzvimbo (Δ A) :
ΔA = β A 1 Δ T
Kupisa kwekupedzisira (T2 ) :
ΔA = β A 1 (T 2 – T 1 )
0,2 masendimita2 = (48 x 10-6 oC-1)(40 cm)2)(T2 - 30oC)
0,2 = (1920 x 10 -6 ) (T 2 - 30 )
0,2 = (1,920 x 10 -3 ) (T 2 - 30)
0,2 = (2 x 10 -3 ) (T 2 - 30)
0,2 / (2 x 10 -3 ) = T 2 – 30
0,1 x 10 3 = T 2 – 30
1 x 10 2 = T 2 – 30
100 = T 2 - 30
100 + 30 = T 2
T 2 = 130
Kupisa kwekupedzisira = 130 o C
3. Chinhu chakatenderera patembiricha ye20 o C chine radius ye20 cm. Kana patembiricha ye100 o C radius ikawedzera kusvika 20,5 cm, saka coefficient yekuwedzera kwemutsara wechinhu chacho….
Kukurukurirana
Zvinozivikanwa kuti:
Tembiricha yekutanga (T 1 ) = 30 o C
Kupisa kwekupedzisira (T2 ) = 100 o C
Kuchinja kwetembiricha (Δ T) = 100 o C – 30 o C = 70 o C
Nharaunda yekutanga (r 1 ) = 20 cm
Radiyo yekupedzisira (r 2 ) = 20,5 cm
Mubvunzo: Kukura kwenzvimbo kwechinhu ( b ) mukoefficient (coefficient)
Mhinduro:
Nzvimbo yekutanga yedenderedzwa (A 1 ) = π r 1 2 = (3,14)(20 cm) 2 = (3,14)(400 cm 2 ) = 1256 cm 2
Nzvimbo yekupedzisira yedenderedzwa (A 2 ) = π r 2 2 = (3,14)(20,5 cm) 2 = (3,14)(420,25 cm 2 ) = 1319,585 cm 2
Kuwedzera kwenzvimbo yedenderedzwa (Δ A) = 1319,585 cm 2 – 1256 cm 2 = 63,585 cm 2
Fomura yekuchinja nzvimbo (Δ A) :
ΔA = β A 1 ΔT
Chiyero chekuwedzera kwenzvimbo:
ΔA = β A 1 ΔT
63,585 masendimita 2 = β (1 256 cm 2 )(70 o C)
63,585 = β ( 87920 o C)
β = 63,585 / 87920 o C
β = 0,00072 / o C
β = 7,2 x 1 0 -4 / o C
β = 7,2 x 1 0 -4 o C -1
Kuwedzerwa kwemutsetse (α ) muchiyero chekuwedzera (coefficient of linear expansion) (α):
β = 2 α
α = β / 2
α = (7,2 x 1 0 -4 ) / 2
α = 3,6 x 1 0 -4 o C -1
